Optimization Techniques

Statement of an optimization problem, design vector, design constraints, constraint surface, objective function and surfaces, classification; Single variable optimization; multi-variable optimization without constraints, necessary and sufficient conditions for minimum/maximum; Multivariable optimization with equality constraints - solution by method of Lagrange multipliers; Multivariable optimization with inequality constraints, Kuhn-Tucker conditions

Standard form of a linear programming problem, geometry of linear programming problems; Definitions and theorems; Solution of a system of linear simultaneous equations, pivotal reduction of a general system of equations; Motivation to the simplex method, simplex algorithm

Finding initial basic feasible solution by north-west corner rule; Least cost method and Vogel's approximation method; Testing for optimality of balanced transportation problems; Special cases in transportation problem

Sequencing: flow-shop sequencing, n jobs through two machines, n jobs through three machines, two jobs through m machines; Theory of games: introduction to decision theory, minimax (maximin) criterion and optimal strategy; Solution of games with saddle points; rectangular games without saddle points; 2 x 2 games; Dominance principle; m x 2 and 2 x n games - graphical method

Project planning, scheduling and controlling; tools for project management; Critical path method (CPM); Programme evaluation and review technique (PERT); Cost analysis and crashing, resource leveling, updating